Latent Semantic Indexing

Latent Semantic Indexing ( LSI ) is an indexing and retrieval method that uses a mathematical technique called Singular Value Decomposition (SVD) to identify patterns in the relationships between the terms and concepts contained in an unstructured collection of text. LSI is based on the principle that words that are used in the same contexts tend to have similar meanings. A key feature of LSI is its ability to extract the conceptual content of a body of text by establishing associations between those terms that occur in similar contexts.

LSI is also an application of Correspondence Analysis, a multivariate statistical technique developed by Jean-Paul Benzécri in the early 1970s, to a Contingency Table built from word counts in documents.

Called Latent Semantic Indexing because of its ability to correlate semantically related terms that are latent in a collection of text, it was first applied to text at Bell Laboratories in the late 1980s. The method, also called Latent Semantic Analysis (LSA), uncovers the underlying latent semantic structure in the usage of words in a body of text and how it can be used to extract the meaning of the text in response to user queries, commonly referred to as concept searches. Queries, or concept searches, against a set of documents that have undergone LSI will return results that are conceptually similar in meaning to the search criteria even if the results don’t share a specific word or words with the search criteria.

Benefits of LSI

LSI overcomes two of the most severe constraints of Boolean keyword queries: multiple words that have similar meanings (synonymy) and words that have more than one meaning (polysemy). Synonymy and polysemy are often the cause of mismatches in the vocabulary used by the authors of documents and the users of information retrieval systems. As a result, Boolean keyword queries often return irrelevant results and miss information that is relevant.

LSI is also used to perform automated document categorization. In fact, several experiments have demonstrated that there are a number of correlations between the way LSI and humans process and categorize text. Document categorization is the assignment of documents to one or more predefined categories based on their similarity to the conceptual content of the categories. LSI uses example documents to establish the conceptual basis for each category. During categorization processing, the concepts contained in the documents being categorized are compared to the concepts contained in the example items, and a category (or categories) is assigned to the documents based on the similarities between the concepts they contain and the concepts that are contained in the example documents.

Dynamic clustering based on the conceptual content of documents can also be accomplished using LSI. Clustering is a way to group documents based on their conceptual similarity to each other without using example documents to establish the conceptual basis for each cluster. This is very useful when dealing with an unknown collection of unstructured text.

Because it uses a strictly mathematical approach, LSI is inherently independent of language. This enables LSI to elicit the semantic content of information written in any language without requiring the use of auxiliary structures, such as dictionaries and thesauri. LSI can also perform cross-linguistic concept searching and example-based categorization. For example, queries can be made in one language, such as English, and conceptually similar results will be returned even if they are composed of an entirely different language or of multiple languages.

LSI is not restricted to working only with words. It can also process arbitrary character strings. Any object that can be expressed as text can be represented in an LSI vector space. For example, tests with MEDLINE abstracts have shown that LSI is able to effectively classify genes based on conceptual modeling of the biological information contained in the titles and abstracts of the MEDLINE citations.

LSI automatically adapts to new and changing terminology, and it has been shown to be very tolerant of noise (i.e., misspelled words, typographical errors, unreadable characters, etc.). This is especially important for applications using text derived from Optical Character Recognition (OCR) and speech-to-text conversion. LSI also deals effectively with sparse, ambiguous, and contradictory data.

Text does not need to be in sentence form for LSI to be effective. It can work with lists, free-form notes, email, Web-based content, etc. As long as a collection of text contains multiple terms, LSI can be used to identify patterns in the relationships between the important terms and concepts contained in the text.

LSI has proven to be a useful solution to a number of conceptual matching problems. The technique has been shown to capture key relationship information, including causal, goal-oriented, and taxonomic information.

LSI Timeline

Mid-1960s – Factor analysis technique first described and tested (H. Borko and M. Bernick)

1988 – Seminal paper on LSI technique published (Deerwester et al.)

1989 – Original patent granted (Deerwester et al.)

1992 – First use of LSI to assign articles to reviewers (Dumais and Nielsen)

1994 – Patent granted for the cross-lingual application of LSI (Landauer et al.)

1998 – First use of LSI for grading essays (Landauer et al.)

1999 – First implementation of LSI technology for intelligence community for analyzing unstructured text (SAIC).

2002 – LSI-based product offering to intelligence-based government agencies (SAIC)

2004 – First commercial use of LSI for essay scoring (SAIC)

2005 – First vertical-specific application – publishing – EDB (EBSCO, Content Analyst Company)

Mathematics of LSI

LSI uses common linear algebra techniques to learn the conceptual correlations in a collection of text. In general, the process involves constructing a weighted term-document matrix, performing a Singular Value Decomposition on the matrix, and using the matrix to identify the concepts contained in the text.

Term Document Matrix

LSI begins by constructing a term-document matrix, A , to identify the occurrences of the m unique terms within a collection of n documents. In a term-document matrix, each term is represented by a row, and each document is represented by a column, with each matrix cell, a _ij , initially representing the number of times the associated term appears in the indicated document, tf _ij . This matrix is usually very large and very sparse.

Once a term-document matrix is constructed, local and global weighting functions can be applied to it to condition the data. The weighting functions transform each cell, a _ij of A , to be the product of a local term weight, l _ij , which describes the relative frequency of a term in a document, and a global weight , g _i , which describes the relative frequency of the term within the entire collection of documents.

Some common local weighting functions are defined in the following table.

Some common global weighting functions are defined in the following table.

Empirical studies with LSI report that the Log Entropy weighting functions work well, in practice, with many data sets. In other words, each entry a _ij of A is computed as:

Rank-Reduced Singular Value Decomposition

A rank-reduced, Singular Value Decomposition is performed on the matrix to determine patterns in the relationships between the terms and concepts contained in the text. The SVD forms the foundation for LSI. It computes the term and document vector spaces by transforming the single term-frequency matrix, A , into three other matrices— a term-concept vector matrix, T , a singular values matrix, S , and a concept-document vector matrix, D , which satisfy the following relations:

In the formula, A , is the supplied m by n weighted matrix of term frequencies in a collection of text where m is the number of unique terms, and n is the number of documents. T is a computed m by r matrix of term vectors where r is the rank of A —a measure of its unique dimensions ≤ min( m,n ) . S is a computed r by r diagonal matrix of decreasing singular values, and D is a computed n by r matrix of document vectors.

The LSI modification to a standard SVD is to reduce the rank or truncate the singular value matrix S to size k « 

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